Time allowed: 60 minutes. Answer ALL 25 questions. Write your answers in the spaces provided. You are NOT allowed to use a calculator. You must show all your working; marks are available for a correct method as well as for the final answer. The number of marks for each question, or part-question, is shown in brackets. This fifth Core (Level 2) paper covers the same breadth as Papers 1-4: number, fractions/decimals/percentages, ratio, algebra, geometry, measures, coordinates, statistics and probability, with entirely different questions.
1
Write the number three hundred and fifty-two thousand and eighty-nine in figures. (1 mark)
(Total for Question 1 is 1 mark)
2
Work out 9002 - 3847 (1 mark)
(Total for Question 2 is 1 mark)
3
Find 3/5 of 85 (1 mark)
(Total for Question 3 is 1 mark)
4
Three angles meet at a point. They are 110 degrees, 145 degrees and k degrees. Work out the size of angle k (1 mark)
(Total for Question 4 is 1 mark)
5
Simplify 6c + 5d - 2c + 3d (1 mark)
(Total for Question 5 is 1 mark)
6
One night in Braemar, the temperature was -8 degrees C. Overnight it fell further by 6 degrees C. Work out the temperature after it fell. (2 marks)
(Total for Question 6 is 2 marks)
7
Convert 21/25 to a percentage. (2 marks)
(Total for Question 7 is 2 marks)
8
Simplify the ratio 56:84 fully. (2 marks)
(Total for Question 8 is 2 marks)
9
Solve 5x + 8 = 53 (2 marks)
(Total for Question 9 is 2 marks)
10
A parallelogram has a base of 18 cm and a perpendicular height of 7 cm. Work out its area. (2 marks)
(Total for Question 10 is 2 marks)
11
Connor is making a fruit punch and needs 1.8 litres of orange juice. He has five cartons of orange juice, each containing 330 ml. Show working to decide whether he has enough orange juice, and if not, say how much more he needs. (2 marks)
(Total for Question 11 is 2 marks)
12
Point J has coordinates (6, 13) and point K has coordinates (14, 5). Find the coordinates of the midpoint of JK. (2 marks)
(Total for Question 12 is 2 marks)
13
In a maths challenge, five pupils scored the following points: 27, 34, 22, 31, 26. Work out the mean score. (2 marks)
(Total for Question 13 is 2 marks)
14
A jar contains 8 orange sweets, 5 lemon sweets and 7 blackcurrant sweets. Mei takes one sweet from the jar at random.
(a)Find the probability that it is lemon. (1 mark)(1)
(b)Find the probability that it is NOT blackcurrant. (1 mark)(1)
(Total for Question 14 is 2 marks)
15
Write down all the factors of 154 that are also prime numbers. (2 marks)
In triangle LMN, angle L = 37 degrees, angle M = (3x + 8) degrees and angle N = 2x degrees.
(a)Form an equation in x and solve it. (2 marks)(2)
(b)Work out the size of angle N. (1 mark)(1)
(Total for Question 17 is 3 marks)
18
Zara and Kwame share 130 marbles in the ratio 3:7. Work out how many marbles Kwame receives. (3 marks)
(Total for Question 18 is 3 marks)
19
A winter coat costs 68 pounds. In a sale, the price is reduced by 25%. Work out the sale price. (3 marks)
(Total for Question 19 is 3 marks)
20
Mrs Ahmed's garden in Ipswich is a rectangle measuring 16 m by 10 m. A rectangular vegetable patch measuring 6 m by 4 m has been dug in one corner of the garden (the vegetable patch is not lawn).
(a)Work out the area of the whole rectangular garden. (1 mark)(1)
(b)Work out the area of the vegetable patch. (1 mark)(1)
(c)Work out the area of the garden that is lawn (not vegetable patch). (2 marks)(2)
(Total for Question 20 is 4 marks)
21
A pie chart was used to show how 120 students voted for their favourite sport in a survey at a school fair. It shows that they voted for Football (angle 144 degrees), Netball (angle 96 degrees), and Tennis (angle 48 degrees). The rest voted for Athletics.
(a)Work out the angle for the Athletics sector of the pie chart. (2 marks)(2)
(b)Work out how many of the 120 students voted for Athletics. (2 marks)(2)
(Total for Question 21 is 4 marks)
22
Amara is x years old. Her cousin Junior is 4 years older than six times Amara's age. The sum of their ages is 88.
(a)Write down an equation in x to represent this information. (1 mark)(1)
(b)Solve your equation to find Amara's age. (2 marks)(2)
(c)Find Junior's age. (1 mark)(1)
(Total for Question 22 is 4 marks)
23
A stationery shop sells glue sticks for 60p each and highlighters for 90p each. Owen buys 5 glue sticks and 3 highlighters, and pays with a 10 pound note.
(a)Work out the total cost of the glue sticks. (1 mark)(1)
(b)Work out the total cost of the highlighters. (1 mark)(1)
(c)Work out how much change Owen should receive from his 10 pound note. (3 marks)(3)
(Total for Question 23 is 5 marks)
24
A circular pond in a park in York has a diameter of 126 cm. Take π = 22/7.
(a)Work out the radius of the pond. (1 mark)(1)
(b)Work out the circumference of the pond. (2 marks)(2)
(c)A protective cover needs to extend 7 cm out from the edge of the pond all the way round. Work out the diameter of the circle that the cover forms. (2 marks)(2)
(Total for Question 24 is 5 marks)
25
At a summer market, a profit of 600 pounds is shared between the drama club fund and the art club fund in the ratio 7:5.
(a)Work out how much money the drama club fund receives. (2 marks)(2)
(b)The drama club fund then spends 20% of its share on costumes. Work out how much money is spent on costumes. (2 marks)(2)
(c)Work out how much money the drama club fund has left after this spending. (2 marks)(2)
(Total for Question 25 is 6 marks)
Mark scheme · CE.M36 Maths: Full Practice Paper (Core, Non-Calculator, Set 5)
Question 1
B1 352089 cao
Answer: 352089
Question 2
B1 5155 cao
Answer: 5155
Question 3
B1 51 cao
Answer: 51
Question 4
B1 105 (degrees) cao
Answer: 105 degrees
Question 5
B1 4c + 8d cao
Answer: 4c + 8d
Question 6
M1 -8 - 6 (correct method)
A1 -14 (degrees C) cao
Answer: -14 degrees C
Question 7
M1 21/25 = 84/100 or equivalent complete method
A1 84% cao
Answer: 84%
Question 8
M1 divides both parts by a common factor (e.g. by 4 or by 7)
A1 2:3 cao (fully simplified)
Answer: 2:3
Question 9
M1 5x = 45 (subtracts 8 from both sides)
A1 x = 9 cao
Answer: x = 9
Question 10
M1 18 x 7 or equivalent complete method
A1 126 cm2 cao
Answer: 126 cm2
Question 11
M1 5 x 330 = 1650 ml (1.65 litres)
A1 No, he does not have enough; he is 150 ml (0.15 litres) short
Answer: No, he is 150 ml short of the orange juice he needs
Question 12
M1 ((6+14)/2 , (13+5)/2) or equivalent complete method
A1 (10, 9) cao
Answer: (10, 9)
Question 13
M1 27+34+22+31+26 (= 140)
A1 28 (points) cao
Answer: 28 points
Question 14
(a) B1 1/4 oe cao
(a) Answer: 1/4
(b) B1 13/20 oe cao
(b) Answer: 13/20
Question 15
M1 a correct list, or attempt at a list, of the factors of 154
A1 2, 7, 11 (all three, no extras) cao
Answer: 2, 7, 11
Question 16
M1 14x + 21 (correct first expansion)
M1 -4x + 20 (correct second expansion, signs handled correctly)
A1 10x + 41 cao
Answer: 10x + 41
Question 17
(a) M1 37 + (3x+8) + 2x = 180 oe
(a) A1 x = 27 cao
(a) Answer: x = 27
(b) B1 54 (degrees), follow through 2 x their x
(b) Answer: 54 degrees
Question 18
M1 identifies 10 total parts (3 + 7)
M1 130 / 10 (= 13), the value of one part
A1 91 (marbles) cao
Answer: 91 marbles
Question 19
M1 finds 25% of 68 (e.g. 10% = 6.8 and 25% = 6.8 x 2.5 = 17)
M1 68 - 17 (subtracts the discount from the original price)
A1 51 pounds cao
Answer: 51 pounds
Question 20
(a) B1 160 m2 cao
(a) Answer: 160 m2
(b) B1 24 m2 cao
(b) Answer: 24 m2
(c) M1 160 - 24 (follow through their (a) and (b))
(c) A1 136 m2 cao
(c) Answer: 136 m2
Question 21
(a) M1 360 - (144 + 96 + 48)
(a) A1 72 (degrees) cao
(a) Answer: 72 degrees
(b) M1 (their (a) / 360) x 120
(b) A1 24 (students) cao
(b) Answer: 24 students
Question 22
(a) B1 x + (6x + 4) = 88 oe
(a) Answer: x + (6x + 4) = 88
(b) M1 7x + 4 = 88 leading to 7x = 84
(b) A1 x = 12 cao
(b) Answer: 12 years old
(c) B1 76 (follow through 6 x their x + 4)
(c) Answer: 76 years old
Question 23
(a) B1 3.00 pounds (300p) cao
(a) Answer: 3.00 pounds
(b) B1 2.70 pounds (270p) cao
(b) Answer: 2.70 pounds
(c) M1 3.00 + 2.70 (follow through their (a) and (b)), the total cost
(c) M1 10.00 - their total cost
(c) A1 4.30 pounds cao
(c) Answer: 4.30 pounds
Question 24
(a) B1 63 cm cao
(a) Answer: 63 cm
(b) M1 22/7 x 126 (or 2 x 22/7 x 63)
(b) A1 396 cm cao
(b) Answer: 396 cm
(c) M1 126 + 2 x 7 (adds the overhang to both sides of the diameter)
(c) A1 140 cm cao
(c) Answer: 140 cm
Question 25
(a) M1 600 / 12 (= 50), the value of one part (12 total parts)